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(8x+4)x=47
We move all terms to the left:
(8x+4)x-(47)=0
We multiply parentheses
8x^2+4x-47=0
a = 8; b = 4; c = -47;
Δ = b2-4ac
Δ = 42-4·8·(-47)
Δ = 1520
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1520}=\sqrt{16*95}=\sqrt{16}*\sqrt{95}=4\sqrt{95}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{95}}{2*8}=\frac{-4-4\sqrt{95}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{95}}{2*8}=\frac{-4+4\sqrt{95}}{16} $
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